WASHINGTON — Since Carl Icahn, the billionaire investor, was named by President Trump as a special adviser on regulatory matters, he has been busy working behind the scenes to try to revamp an obscure Environmental Protection Agency rule that governs the way corn-based ethanol is mixed into gasoline nationwide.

It is a campaign that fits into the charge Mr. Trump gave Mr. Icahn, to help the nation “break free of excessive regulation.” But there is an additional detail that is raising eyebrows in Washington: Mr. Icahn is a majority investor in CVR Energy,